A controller for following a preceding vehicle and for automatic following of the preceding vehicle is known from, for example, Japanese Kokai Patent Application No. 1999-334552. In that controller, when the vehicle speed falls below a prescribed speed, the control for following the preceding vehicle is released, and only control of the brake force is continued. When the vehicle speed nearly reaches 0, the brake force control is released. Consequently, when the preceding vehicle stops and then moves forward again, it is necessary to brake to keep the automobile stopped, to perform an acceleration operation to move the automobile forward and to perform a switch operation to restart the control for following the preceding vehicle.